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-rw-r--r--numeric.c691
1 files changed, 691 insertions, 0 deletions
diff --git a/numeric.c b/numeric.c
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+++ b/numeric.c
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+/* numeric.c
+ *
+ * Copyright (c) 2001, Larry Wall
+ *
+ * You may distribute under the terms of either the GNU General Public
+ * License or the Artistic License, as specified in the README file.
+ *
+ */
+
+/*
+ * "That only makes eleven (plus one mislaid) and not fourteen, unless
+ * wizards count differently to other people."
+ */
+
+#include "EXTERN.h"
+#define PERL_IN_NUMERIC_C
+#include "perl.h"
+
+U32
+Perl_cast_ulong(pTHX_ NV f)
+{
+ if (f < 0.0)
+ return f < I32_MIN ? (U32) I32_MIN : (U32)(I32) f;
+ if (f < U32_MAX_P1) {
+#if CASTFLAGS & 2
+ if (f < U32_MAX_P1_HALF)
+ return (U32) f;
+ f -= U32_MAX_P1_HALF;
+ return ((U32) f) | (1 + U32_MAX >> 1);
+#else
+ return (U32) f;
+#endif
+ }
+ return f > 0 ? U32_MAX : 0 /* NaN */;
+}
+
+I32
+Perl_cast_i32(pTHX_ NV f)
+{
+ if (f < I32_MAX_P1)
+ return f < I32_MIN ? I32_MIN : (I32) f;
+ if (f < U32_MAX_P1) {
+#if CASTFLAGS & 2
+ if (f < U32_MAX_P1_HALF)
+ return (I32)(U32) f;
+ f -= U32_MAX_P1_HALF;
+ return (I32)(((U32) f) | (1 + U32_MAX >> 1));
+#else
+ return (I32)(U32) f;
+#endif
+ }
+ return f > 0 ? (I32)U32_MAX : 0 /* NaN */;
+}
+
+IV
+Perl_cast_iv(pTHX_ NV f)
+{
+ if (f < IV_MAX_P1)
+ return f < IV_MIN ? IV_MIN : (IV) f;
+ if (f < UV_MAX_P1) {
+#if CASTFLAGS & 2
+ /* For future flexibility allowing for sizeof(UV) >= sizeof(IV) */
+ if (f < UV_MAX_P1_HALF)
+ return (IV)(UV) f;
+ f -= UV_MAX_P1_HALF;
+ return (IV)(((UV) f) | (1 + UV_MAX >> 1));
+#else
+ return (IV)(UV) f;
+#endif
+ }
+ return f > 0 ? (IV)UV_MAX : 0 /* NaN */;
+}
+
+UV
+Perl_cast_uv(pTHX_ NV f)
+{
+ if (f < 0.0)
+ return f < IV_MIN ? (UV) IV_MIN : (UV)(IV) f;
+ if (f < UV_MAX_P1) {
+#if CASTFLAGS & 2
+ if (f < UV_MAX_P1_HALF)
+ return (UV) f;
+ f -= UV_MAX_P1_HALF;
+ return ((UV) f) | (1 + UV_MAX >> 1);
+#else
+ return (UV) f;
+#endif
+ }
+ return f > 0 ? UV_MAX : 0 /* NaN */;
+}
+
+#if defined(HUGE_VAL) || (defined(USE_LONG_DOUBLE) && defined(HUGE_VALL))
+/*
+ * This hack is to force load of "huge" support from libm.a
+ * So it is in perl for (say) POSIX to use.
+ * Needed for SunOS with Sun's 'acc' for example.
+ */
+NV
+Perl_huge(void)
+{
+# if defined(USE_LONG_DOUBLE) && defined(HUGE_VALL)
+ return HUGE_VALL;
+# endif
+ return HUGE_VAL;
+}
+#endif
+
+NV
+Perl_scan_bin(pTHX_ char *start, STRLEN len, STRLEN *retlen)
+{
+ register char *s = start;
+ register NV rnv = 0.0;
+ register UV ruv = 0;
+ register bool seenb = FALSE;
+ register bool overflowed = FALSE;
+
+ for (; len-- && *s; s++) {
+ if (!(*s == '0' || *s == '1')) {
+ if (*s == '_' && len && *retlen
+ && (s[1] == '0' || s[1] == '1'))
+ {
+ --len;
+ ++s;
+ }
+ else if (seenb == FALSE && *s == 'b' && ruv == 0) {
+ /* Disallow 0bbb0b0bbb... */
+ seenb = TRUE;
+ continue;
+ }
+ else {
+ if (ckWARN(WARN_DIGIT))
+ Perl_warner(aTHX_ WARN_DIGIT,
+ "Illegal binary digit '%c' ignored", *s);
+ break;
+ }
+ }
+ if (!overflowed) {
+ register UV xuv = ruv << 1;
+
+ if ((xuv >> 1) != ruv) {
+ overflowed = TRUE;
+ rnv = (NV) ruv;
+ if (ckWARN_d(WARN_OVERFLOW))
+ Perl_warner(aTHX_ WARN_OVERFLOW,
+ "Integer overflow in binary number");
+ }
+ else
+ ruv = xuv | (*s - '0');
+ }
+ if (overflowed) {
+ rnv *= 2;
+ /* If an NV has not enough bits in its mantissa to
+ * represent an UV this summing of small low-order numbers
+ * is a waste of time (because the NV cannot preserve
+ * the low-order bits anyway): we could just remember when
+ * did we overflow and in the end just multiply rnv by the
+ * right amount. */
+ rnv += (*s - '0');
+ }
+ }
+ if (!overflowed)
+ rnv = (NV) ruv;
+ if ( ( overflowed && rnv > 4294967295.0)
+#if UVSIZE > 4
+ || (!overflowed && ruv > 0xffffffff )
+#endif
+ ) {
+ if (ckWARN(WARN_PORTABLE))
+ Perl_warner(aTHX_ WARN_PORTABLE,
+ "Binary number > 0b11111111111111111111111111111111 non-portable");
+ }
+ *retlen = s - start;
+ return rnv;
+}
+
+NV
+Perl_scan_oct(pTHX_ char *start, STRLEN len, STRLEN *retlen)
+{
+ register char *s = start;
+ register NV rnv = 0.0;
+ register UV ruv = 0;
+ register bool overflowed = FALSE;
+
+ for (; len-- && *s; s++) {
+ if (!(*s >= '0' && *s <= '7')) {
+ if (*s == '_' && len && *retlen
+ && (s[1] >= '0' && s[1] <= '7'))
+ {
+ --len;
+ ++s;
+ }
+ else {
+ /* Allow \octal to work the DWIM way (that is, stop scanning
+ * as soon as non-octal characters are seen, complain only iff
+ * someone seems to want to use the digits eight and nine). */
+ if (*s == '8' || *s == '9') {
+ if (ckWARN(WARN_DIGIT))
+ Perl_warner(aTHX_ WARN_DIGIT,
+ "Illegal octal digit '%c' ignored", *s);
+ }
+ break;
+ }
+ }
+ if (!overflowed) {
+ register UV xuv = ruv << 3;
+
+ if ((xuv >> 3) != ruv) {
+ overflowed = TRUE;
+ rnv = (NV) ruv;
+ if (ckWARN_d(WARN_OVERFLOW))
+ Perl_warner(aTHX_ WARN_OVERFLOW,
+ "Integer overflow in octal number");
+ }
+ else
+ ruv = xuv | (*s - '0');
+ }
+ if (overflowed) {
+ rnv *= 8.0;
+ /* If an NV has not enough bits in its mantissa to
+ * represent an UV this summing of small low-order numbers
+ * is a waste of time (because the NV cannot preserve
+ * the low-order bits anyway): we could just remember when
+ * did we overflow and in the end just multiply rnv by the
+ * right amount of 8-tuples. */
+ rnv += (NV)(*s - '0');
+ }
+ }
+ if (!overflowed)
+ rnv = (NV) ruv;
+ if ( ( overflowed && rnv > 4294967295.0)
+#if UVSIZE > 4
+ || (!overflowed && ruv > 0xffffffff )
+#endif
+ ) {
+ if (ckWARN(WARN_PORTABLE))
+ Perl_warner(aTHX_ WARN_PORTABLE,
+ "Octal number > 037777777777 non-portable");
+ }
+ *retlen = s - start;
+ return rnv;
+}
+
+NV
+Perl_scan_hex(pTHX_ char *start, STRLEN len, STRLEN *retlen)
+{
+ register char *s = start;
+ register NV rnv = 0.0;
+ register UV ruv = 0;
+ register bool overflowed = FALSE;
+ char *hexdigit;
+
+ if (len > 2) {
+ if (s[0] == 'x') {
+ s++;
+ len--;
+ }
+ else if (len > 3 && s[0] == '0' && s[1] == 'x') {
+ s+=2;
+ len-=2;
+ }
+ }
+
+ for (; len-- && *s; s++) {
+ hexdigit = strchr((char *) PL_hexdigit, *s);
+ if (!hexdigit) {
+ if (*s == '_' && len && *retlen && s[1]
+ && (hexdigit = strchr((char *) PL_hexdigit, s[1])))
+ {
+ --len;
+ ++s;
+ }
+ else {
+ if (ckWARN(WARN_DIGIT))
+ Perl_warner(aTHX_ WARN_DIGIT,
+ "Illegal hexadecimal digit '%c' ignored", *s);
+ break;
+ }
+ }
+ if (!overflowed) {
+ register UV xuv = ruv << 4;
+
+ if ((xuv >> 4) != ruv) {
+ overflowed = TRUE;
+ rnv = (NV) ruv;
+ if (ckWARN_d(WARN_OVERFLOW))
+ Perl_warner(aTHX_ WARN_OVERFLOW,
+ "Integer overflow in hexadecimal number");
+ }
+ else
+ ruv = xuv | ((hexdigit - PL_hexdigit) & 15);
+ }
+ if (overflowed) {
+ rnv *= 16.0;
+ /* If an NV has not enough bits in its mantissa to
+ * represent an UV this summing of small low-order numbers
+ * is a waste of time (because the NV cannot preserve
+ * the low-order bits anyway): we could just remember when
+ * did we overflow and in the end just multiply rnv by the
+ * right amount of 16-tuples. */
+ rnv += (NV)((hexdigit - PL_hexdigit) & 15);
+ }
+ }
+ if (!overflowed)
+ rnv = (NV) ruv;
+ if ( ( overflowed && rnv > 4294967295.0)
+#if UVSIZE > 4
+ || (!overflowed && ruv > 0xffffffff )
+#endif
+ ) {
+ if (ckWARN(WARN_PORTABLE))
+ Perl_warner(aTHX_ WARN_PORTABLE,
+ "Hexadecimal number > 0xffffffff non-portable");
+ }
+ *retlen = s - start;
+ return rnv;
+}
+
+/*
+=for apidoc grok_numeric_radix
+
+Scan and skip for a numeric decimal separator (radix).
+
+=cut
+ */
+bool
+Perl_grok_numeric_radix(pTHX_ const char **sp, const char *send)
+{
+#ifdef USE_LOCALE_NUMERIC
+ if (PL_numeric_radix_sv && IN_LOCALE) {
+ STRLEN len;
+ char* radix = SvPV(PL_numeric_radix_sv, len);
+ if (*sp + len <= send && memEQ(*sp, radix, len)) {
+ *sp += len;
+ return TRUE;
+ }
+ }
+ /* always try "." if numeric radix didn't match because
+ * we may have data from different locales mixed */
+#endif
+ if (*sp < send && **sp == '.') {
+ ++*sp;
+ return TRUE;
+ }
+ return FALSE;
+}
+
+/*
+=for apidoc grok_number
+
+Recognise (or not) a number. The type of the number is returned
+(0 if unrecognised), otherwise it is a bit-ORed combination of
+IS_NUMBER_IN_UV, IS_NUMBER_GREATER_THAN_UV_MAX, IS_NUMBER_NOT_INT,
+IS_NUMBER_NEG, IS_NUMBER_INFINITY (defined in perl.h). If the value
+of the number can fit an in UV, it is returned in the *valuep.
+
+=cut
+ */
+int
+Perl_grok_number(pTHX_ const char *pv, STRLEN len, UV *valuep)
+{
+ const char *s = pv;
+ const char *send = pv + len;
+ const UV max_div_10 = UV_MAX / 10;
+ const char max_mod_10 = UV_MAX % 10 + '0';
+ int numtype = 0;
+ int sawinf = 0;
+
+ while (isSPACE(*s))
+ s++;
+ if (*s == '-') {
+ s++;
+ numtype = IS_NUMBER_NEG;
+ }
+ else if (*s == '+')
+ s++;
+
+ /* next must be digit or the radix separator or beginning of infinity */
+ if (isDIGIT(*s)) {
+ /* UVs are at least 32 bits, so the first 9 decimal digits cannot
+ overflow. */
+ UV value = *s - '0';
+ /* This construction seems to be more optimiser friendly.
+ (without it gcc does the isDIGIT test and the *s - '0' separately)
+ With it gcc on arm is managing 6 instructions (6 cycles) per digit.
+ In theory the optimiser could deduce how far to unroll the loop
+ before checking for overflow. */
+ int digit = *++s - '0';
+ if (digit >= 0 && digit <= 9) {
+ value = value * 10 + digit;
+ digit = *++s - '0';
+ if (digit >= 0 && digit <= 9) {
+ value = value * 10 + digit;
+ digit = *++s - '0';
+ if (digit >= 0 && digit <= 9) {
+ value = value * 10 + digit;
+ digit = *++s - '0';
+ if (digit >= 0 && digit <= 9) {
+ value = value * 10 + digit;
+ digit = *++s - '0';
+ if (digit >= 0 && digit <= 9) {
+ value = value * 10 + digit;
+ digit = *++s - '0';
+ if (digit >= 0 && digit <= 9) {
+ value = value * 10 + digit;
+ digit = *++s - '0';
+ if (digit >= 0 && digit <= 9) {
+ value = value * 10 + digit;
+ digit = *++s - '0';
+ if (digit >= 0 && digit <= 9) {
+ value = value * 10 + digit;
+ /* Now got 9 digits, so need to check
+ each time for overflow. */
+ digit = *++s - '0';
+ while (digit >= 0 && digit <= 9
+ && (value < max_div_10
+ || (value == max_div_10
+ && *s <= max_mod_10))) {
+ value = value * 10 + digit;
+ digit = *++s - '0';
+ }
+ if (digit >= 0 && digit <= 9) {
+ /* value overflowed.
+ skip the remaining digits, don't
+ worry about setting *valuep. */
+ do {
+ s++;
+ } while (isDIGIT(*s));
+ numtype |=
+ IS_NUMBER_GREATER_THAN_UV_MAX;
+ goto skip_value;
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+ numtype |= IS_NUMBER_IN_UV;
+ if (valuep)
+ *valuep = value;
+
+ skip_value:
+ if (GROK_NUMERIC_RADIX(&s, send)) {
+ numtype |= IS_NUMBER_NOT_INT;
+ while (isDIGIT(*s)) /* optional digits after the radix */
+ s++;
+ }
+ }
+ else if (GROK_NUMERIC_RADIX(&s, send)) {
+ numtype |= IS_NUMBER_NOT_INT;
+ /* no digits before the radix means we need digits after it */
+ if (isDIGIT(*s)) {
+ do {
+ s++;
+ } while (isDIGIT(*s));
+ numtype |= IS_NUMBER_IN_UV;
+ if (valuep) {
+ /* integer approximation is valid - it's 0. */
+ *valuep = 0;
+ }
+ }
+ else
+ return 0;
+ }
+ else if (*s == 'I' || *s == 'i') {
+ s++; if (*s != 'N' && *s != 'n') return 0;
+ s++; if (*s != 'F' && *s != 'f') return 0;
+ s++; if (*s == 'I' || *s == 'i') {
+ s++; if (*s != 'N' && *s != 'n') return 0;
+ s++; if (*s != 'I' && *s != 'i') return 0;
+ s++; if (*s != 'T' && *s != 't') return 0;
+ s++; if (*s != 'Y' && *s != 'y') return 0;
+ s++;
+ }
+ sawinf = 1;
+ }
+ else /* Add test for NaN here. */
+ return 0;
+
+ if (sawinf) {
+ numtype &= IS_NUMBER_NEG; /* Keep track of sign */
+ numtype |= IS_NUMBER_INFINITY | IS_NUMBER_NOT_INT;
+ } else {
+ /* we can have an optional exponent part */
+ if (*s == 'e' || *s == 'E') {
+ /* The only flag we keep is sign. Blow away any "it's UV" */
+ numtype &= IS_NUMBER_NEG;
+ numtype |= IS_NUMBER_NOT_INT;
+ s++;
+ if (*s == '-' || *s == '+')
+ s++;
+ if (isDIGIT(*s)) {
+ do {
+ s++;
+ } while (isDIGIT(*s));
+ }
+ else
+ return 0;
+ }
+ }
+ while (isSPACE(*s))
+ s++;
+ if (s >= send)
+ return numtype;
+ if (len == 10 && memEQ(pv, "0 but true", 10)) {
+ if (valuep)
+ *valuep = 0;
+ return IS_NUMBER_IN_UV;
+ }
+ return 0;
+}
+
+NV
+S_mulexp10(NV value, I32 exponent)
+{
+ NV result = 1.0;
+ NV power = 10.0;
+ bool negative = 0;
+ I32 bit;
+
+ if (exponent == 0)
+ return value;
+ else if (exponent < 0) {
+ negative = 1;
+ exponent = -exponent;
+ }
+ for (bit = 1; exponent; bit <<= 1) {
+ if (exponent & bit) {
+ exponent ^= bit;
+ result *= power;
+ }
+ power *= power;
+ }
+ return negative ? value / result : value * result;
+}
+
+NV
+Perl_my_atof(pTHX_ const char* s)
+{
+ NV x = 0.0;
+#ifdef USE_LOCALE_NUMERIC
+ if (PL_numeric_local && IN_LOCALE) {
+ NV y;
+
+ /* Scan the number twice; once using locale and once without;
+ * choose the larger result (in absolute value). */
+ Perl_atof2(aTHX_ s, &x);
+ SET_NUMERIC_STANDARD();
+ Perl_atof2(aTHX_ s, &y);
+ SET_NUMERIC_LOCAL();
+ if ((y < 0.0 && y < x) || (y > 0.0 && y > x))
+ return y;
+ }
+ else
+ Perl_atof2(aTHX_ s, &x);
+#else
+ Perl_atof2(aTHX_ s, &x);
+#endif
+ return x;
+}
+
+char*
+Perl_my_atof2(pTHX_ const char* orig, NV* value)
+{
+ NV result = 0.0;
+ bool negative = 0;
+ char* s = (char*)orig;
+ char* send = s + strlen(orig) - 1;
+ bool seendigit = 0;
+ I32 expextra = 0;
+ I32 exponent = 0;
+ I32 i;
+/* this is arbitrary */
+#define PARTLIM 6
+/* we want the largest integers we can usefully use */
+#if defined(HAS_QUAD) && defined(USE_64_BIT_INT)
+# define PARTSIZE ((int)TYPE_DIGITS(U64)-1)
+ U64 part[PARTLIM];
+#else
+# define PARTSIZE ((int)TYPE_DIGITS(U32)-1)
+ U32 part[PARTLIM];
+#endif
+ I32 ipart = 0; /* index into part[] */
+ I32 offcount; /* number of digits in least significant part */
+
+ /* sign */
+ switch (*s) {
+ case '-':
+ negative = 1;
+ /* fall through */
+ case '+':
+ ++s;
+ }
+
+ part[0] = offcount = 0;
+ if (isDIGIT(*s)) {
+ seendigit = 1; /* get this over with */
+
+ /* skip leading zeros */
+ while (*s == '0')
+ ++s;
+ }
+
+ /* integer digits */
+ while (isDIGIT(*s)) {
+ if (++offcount > PARTSIZE) {
+ if (++ipart < PARTLIM) {
+ part[ipart] = 0;
+ offcount = 1; /* ++0 */
+ }
+ else {
+ /* limits of precision reached */
+ --ipart;
+ --offcount;
+ if (*s >= '5')
+ ++part[ipart];
+ while (isDIGIT(*s)) {
+ ++expextra;
+ ++s;
+ }
+ /* warn of loss of precision? */
+ break;
+ }
+ }
+ part[ipart] = part[ipart] * 10 + (*s++ - '0');
+ }
+
+ /* decimal point */
+ if (GROK_NUMERIC_RADIX((const char **)&s, send)) {
+ if (isDIGIT(*s))
+ seendigit = 1; /* get this over with */
+
+ /* decimal digits */
+ while (isDIGIT(*s)) {
+ if (++offcount > PARTSIZE) {
+ if (++ipart < PARTLIM) {
+ part[ipart] = 0;
+ offcount = 1; /* ++0 */
+ }
+ else {
+ /* limits of precision reached */
+ --ipart;
+ --offcount;
+ if (*s >= '5')
+ ++part[ipart];
+ while (isDIGIT(*s))
+ ++s;
+ /* warn of loss of precision? */
+ break;
+ }
+ }
+ --expextra;
+ part[ipart] = part[ipart] * 10 + (*s++ - '0');
+ }
+ }
+
+ /* combine components of mantissa */
+ for (i = 0; i <= ipart; ++i)
+ result += S_mulexp10((NV)part[ipart - i],
+ i ? offcount + (i - 1) * PARTSIZE : 0);
+
+ if (seendigit && (*s == 'e' || *s == 'E')) {
+ bool expnegative = 0;
+
+ ++s;
+ switch (*s) {
+ case '-':
+ expnegative = 1;
+ /* fall through */
+ case '+':
+ ++s;
+ }
+ while (isDIGIT(*s))
+ exponent = exponent * 10 + (*s++ - '0');
+ if (expnegative)
+ exponent = -exponent;
+ }
+
+ /* now apply the exponent */
+ exponent += expextra;
+ result = S_mulexp10(result, exponent);
+
+ /* now apply the sign */
+ if (negative)
+ result = -result;
+ *value = result;
+ return s;
+}
+
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